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AZSV-7 



U S D£PT. OF AGRICULTURE 

p. R ft R Y 



Buying Versus Renting a Combine f eb 1 4 1962 



A Suggested Basis for Decision Mak 
By Edward J. Smith 



.ing 



CURRENT SPRIAI RECORDS 



From time to time, many farm operators are faced with a choice between buying one of 
several types and sizes of combines and hiring a custom machine. Heretofore, research 
studies designed to aid farmers in making sound decisions of this type have considered 
primarily the effect of annual use, or acreage harvested, on the costs of the various alter- 
natives. This conventional analysis attempts to determine the annual acreage required to 
justify, on a cost basis, the purchase of a combine. Below this acreage, the hiring of a 
custom combine is more economical. Labor is usually valued at the going wage rate paid 
farm help in the area, and interest on investment is based on rates that local farmers pay 
for borrowed funds. This article points out why the conventional analysis often proves 
inadequate, and suggests a simple way in which these difficulties may be overcome by 
taking other important variables into account. While the suggested procedure is applied 
here to the problem of choosing the least-cost method of combining grain, it should prove 
equally useful for other economic problems of this type. The generous assistance of 
I. R. Starbird and E. L. Langsford, Farm Economics Division, Economic Research Serv- 
ice, who made available to the author data and specialized knowledge of the Mississippi 
Delta area, is gratefully acknowledged. The article has also benefited greatly from the 
comments and suggestions of R. V. Baumann, J. J. Csorba, A. S. Fox, M. S. Parsons, 
and M. L. Upchurch, Farm Economics Division, Economic Research Service. 



T N THE MISSISSIPPI DELTA, oats and soy- 
beans are the chief crops harvested with com- 
bines. This analysis applies to a farm situation 
that is commonly found in the area -where both of 
these crops are grown and where the soybean 
acreage equals or to some extent exceeds that of 
oats. 

These farm operators can choose between hiring 
a custom combine, buying one or two 7-foot power- 
takeoff machines, or buying a 12-foot self propelled 
combine. This article is designed to show under 
what conditions (acreage, cost of labor, or cost of 
capital) each of these methods is the least-cost 
choice. It is assumed that custom machines are 



available when needed, and that the quality of the 
job they do is comparable to that done with either 
size of owned combine. For the sake of simplicity, 
it is also assumed that the custom rate per acre is 
the same regardless of number of acres harvested. 
Depreciation costs of the owned machines are 
based on a useful life of 10 years. 

The cost data and performance rates are based 
on unpublished data from a 1959 survey in the 
Mississippi Delta, made by Irving Starbird of the 
Economic Eesearch Service (table 1). Per acre 
costs are calculated for a wide range of annual 
harvested acreages. The fixed and variable cost 
components and their total are shown in table 2. 



Reprinted from the Agricultural Economics Research, a journal of economic 
and statistical research, United States Department of Agriculture and coopera- 
tingagencies, Volume XIII, Number 4, October 1961, bythe Economic Research 

Service. 



December 1961 
ERS-46 



109 



The Conventional Analysis 

For illustrative purposes, interest on investment 
is charged at 5 percent, and labor is valued at $1 
an hour. At these cost rates, the competitive posi- 
tion of the various alternatives can readily be 
shown in chart form (fig. 1). The least-cost 
method for a given acreage is easily determined — 
it is always the bottom line at that point (acreage) 
on the chart. In the present case, the least-cost 
alternative is custom combining up to about 94 
acres per year. Above this point, the overhead 
costs of an owned 7-foot power-takeoff machine 
are spread over enough acres so that this machine 
takes over as the least-cost choice and holds its 
advantage up to its maximum annual capacity 
(250 acres) - 1 

But what if the operator's risk aversion is such 
that he prefers to keep a little more excess capacity 
available, even at a somewhat higher per unit cost? 
If he is reluctant to try to handle more than, say, 
200 acres with a single 7-foot machine, he may 
choose to buy the 12-foot self-propelled machine, 
since it is the next-to-lowest cost method. Under 
these cost conditions, two 7-foot combines do not 
become the most economical alternative at any 
point. 

This is essentially the conventional type of 
analysis of the problem. The method has useful- 
ness in the case of a single farm, or for a homo- 
geneous group of farms with the appropriate 
opportunity cost of labor and capital approxi- 
mately the same for each farm in the group. This 
might be the case with a group of farms when 
the purchase of a combine involves borrowing 
money and hiring extra help during the harvest 
season, with both freely available at the standard 
rate — that is, having no important competing 
uses. 

But this is not the usual case. There are a great 
many farm situations to which the prevailing rates 
of wages and interest do not apply. Unless com- 
petent hired help is readily available during the 



Table 1. — Performance rates and costs for 7-foot 
potoer-takeoff and 12- foot self-propelled com- 
bines, Mississippi Delta 1 



1 Capacity limits of 250 acres for the 7-foot power- 
takeoff combine and 500 acres for the 12-foot self-propelled 
machine are based on estimates made by those who are 
thoroughly familiar with harvesting conditions in the 
Delta areas. They reflect acreages that can be handled in 
all except the most unfavorable seasons with reasonable 
timeliness so that serious harvesting losses are not 
encountered. 



Item 


Unit 


7-foot 
combine 


12-foot 
combine 


Capacity per hour 
Labor per acre _ _ . 
Costs: 

Fixed costs per year: 

Depreciation. 

Other 


Acre . _ 
Man-hour. . 

Dollar . .. 
...do 


1.0 
1.0 

180. 00 
70.00 


2. 
. 5 

472. 50 
183. 75 




...do 




Total 


250. 00 


656. 25 




...do 

...do 

...do 




Variable costs per 
acre: 
Combine operating 

costs. 
Tractor operating 
costs. 
Total 


1. 23 

. 60 

1. 83 


1. 40 
1. 40 



1 Based on unpublished data from a 1959 survey in the 
Mississippi Delta by Irving Starbird, Farm Economics 
Division, ERS, USDA. Costs and labor requirements for 
hauling and storing the combined grain are not included 
under either of the above methods, nor are they covered 
by the custom rates used. 



harvest season, the appropriate value of the farm- 
er's labor is more likely to be what it can earn in 
a competing use. Neither can one safely assume 
that additional capital is available to each farmer 
in the group at essentially the same rate. Volun- 
tary or involuntary capital rationing is more 
likely to be found in varying degree within any 
otherwise homogeneous group of farms. Farm 
operators are usually able (or willing) to borrow 
only limited amounts of money. 

The question then arises, Will some competing 
use of the borrowed funds be more profitable than 
investing them in a combine? This means that 
a single chart seldom has general applicability. 
For analysis, a separate chart is required for each 
combination of capital and labor cost rates (op- 
portunity costs). This is a serious limitation in 
demonstrating how variations in the opportunity 
costs of labor and capital affect the choice of the 
least-cost method of combining. 

The Suggested Procedure With Two 
Alternatives 

However, the "break-even points" of the con- 
ventional analysis provide a ready means of gen- 
eralizing the charts. By so doing, with only a few 
charts, the least-cost method can be readily de- 
termined for many combinations of capital and 



110 



Table 2. — Per acre costs of comforting with one 7-foot power-takeoff combine, two 7-foot power-takeoff 
combines, and one 12-foot self -propelled combine, with labor valued at$l an hour, specified acreages, 
Mississippi Delta 



Acres 


One 


7-foot combine 


Two 


7-foot combines 


One 12-foot combine 


harvested 
per year 


Fixed 

costs per 

acre ' 


Variable 

costs per 
acre 


Total 

costs per 

acre 


Fixed 

costs per 

acre l 


Variable 

costs per 

acre 


Total 

costs per 

acre 


Fixed 

costs per 
acre 1 


Variable 

costs per 

acre 


Total 

costs per 

acre 


25 


Dollars 
10.00 
5.00 
3.33 
2.50 
2. 00 
1. 67 
1.43 
1. 25 
1. 00 


Dollars 
2. 83 
2.83 
2.83 
2.83 
2. 83 
2.83 
2.83 
2.83 
2. S3 


Dollars 
12. S3 
7. 83 
6. 16 
5.33 
4 83 
4. 50 
4 26 
4.08 
3.83 


Dollars 


Dollars 


Dollars 


Dollars 
26. 25 
13. 12 
8. 75 
6. 56 
5. 25 
4 38 
3. 75 
3. 27 
2. 62 
2. 19 
1.88 
1. 64 
1. 46 
1.31 


Dollars 
1.90 
1. 90 
1.90 
1.90 
1. 90 
1.90 
1.90 
1. 90 
1.90 
1.90 
1.90 
1. 90 
1.90 
1.90 


Dollars 
28. 15 


50 








15. 02 


75 - 








10. 65 


100 








8. 46 


125 








7. 15 


150 








6.28 


175 








5.65 


200 


2. 50 
2.00 
1. 67 
1.43 
1. 25 
1. 11 
1.00 


2. 83 
2.83 
2. 83 
2. 83 
2. 83 
2. 83 
2.83 


5.33 
4 83 
4 50 
4 26 
4.08 
3.94 
3. 83 


5. 17 


250. . 


4.52 


300. 


4.09 


350 








3. 78 


400 








3. 54 


450.- 








3. 36 


500 .- 






3. 21 











1 It is assumed that each combine can be used 2,500 hours but will be obsolete at the end of 10 years. Depreciation 
thus becomes a variable cost if the machine receives 2,500 hours of use before the end of the 10-year period. 



labor cost rates and the principles of choice illus- 
trated. 2 In an attempt to make the development 
easy to follow, we go from the conventional anal- 
ysis to the more generalized one step by step. For 
the same reason, we first present an arithmetic 
example before developing the algebra, and illus- 
trate its application with only two alternatives 
before applying it to all four possibilities. 



3 A single 3-dimensional model might be used effectively 
under some circumstances. This might be viewed from 
above, with the value of labor along one axis and the in- 
terest rate along the perpendicular axis. The height of 
the surface would then indicate the break-even acreage for 
the various combinations of capital and labor cost, and 
could be shown on 2-dimensional paper as acreage figures 
written in at the intersection of the appropriate wage and 
interest rates. The use of such a model presents several 
problems here, however. One difficulty is that the inde- 
terminancy of the capacity limit cannot readily be shown. 
Another is the problem of showing, in a limited space, 
both the height of the "roof" and the identity of the least- 
cost zone that is above this roof and the one that is below 
it (since the roof, or surface, itself represents the break- 
even acreage). Finally, we see no very practical way of 
representing a double "roof," such as we have in the right- 
hand portions of both the upper and lower sections of 
fig. 3. Such a 3-dimensional model could be used quite 
effectively with only 2 alternatives, but with the four we 
are comparing here, it would seem more practical to use 
several 2-dimensional charts. 



To illustrate the possibilities of the new proce- 
dure, we return to figure 1. With a custom rate 
of $5.50 per acre, the break-even point with a 
7-foot power-takeoff combine comes at about 94 
acres ; that is, at this acreage it costs the same by 
either method. Algebraically, this break-even 
point can be determined rather easily. If we let 
A stand for the annual harvested acreage, the 
right side of the following equation simply means 
that the total cost per acre with a 7-foot power- 
takeoff combine is the sum of the fixed cost per 
acre ($250/A) plus the operating costs per acre 
($1.83), plus the labor cost per acre (1 hour per 
acre at $1.00 an hour). All that is needed is to 
find the number of acres that will make this sum 
equal $5.50. 

That is : 



Or, 



5.50=250/A+ 1.83 + 1 (1.00) 
250/A=2.67 



Solving, 



A=93.6. 



This is the break-even acreage for a labor rate 
of $1 an hour. To generalize the analysis, various 
labor rates are substituted into the equation, and 



111 



COSTS PER ACRE FOR COMBINING, 
MISSISSIPPI DELTA 



DOLLARS 



6.00 



4.00 



2.00 




One 7' PTO 
combine (owned) 



J__ i 



Two 7' PTO combines (owned) 



J 1 



J I 



100 



200 300 400 

ACRES HARVESTED PER YEAR 



500 



U. S. DEPARTMENT OF AGRICULTURE 



NEC ERS 419-61 (8) ECONOMIC RESEARCH SERVICE 



Figure 1. 



each is solved for the break-even acreage. 3 When 
these points are plotted on a graph such as figure 
2 and connected by a line, they separate those 
combinations of labor rates and acreage for which 
custom combining is cheaper and those for which 



8 To do this, we use the following notation : 

Vi=: variable costs per acre of custom combining; 
that is, the custom rate per acre 

F 2 = annual fixed cost of the owned combine (depre- 
ciation, interest, taxes, insurance, and 
housing) 

V a = variable or operating costs per acre of the owned 
combine and tractor 

La= labor requirements in hours per acre with the 
owned combine 

W= the value of labor per hour 
Then the above equation can be represented in more gen- 
eral form as : 

V 1 =F 2 /A+V2+L 2 W 
To enable us to solve for A more conveniently, this can 
be rewritten as : 

A= _ 3. 

V!— V a -L 2 W 



it costs less to own a combine. For all acreage 
and labor-rate combinations to the left of and 
above the line in figure 2, the less costly alter- 
native is to hire a custom combine, while for all 
combinations to the right of and below the line, 
it costs less to own a 7-foot power-takeoff com- 
bine. The clear area at the right-hand edge of 
the chart indicates the approximate capacity limit 
of the machine for a farm operator with a medium 
degree of risk aversion. 

For extremely low labor rates, the costs of the 
two methods are approximately equal at about 75 
acres. But the use of his own combine takes more 
of the farmer's labor than hiring a custom ma- 
chine. Therefore, as the labor rates go up, so 
does the per acre cost of using his own combine. 
Thus, the competitive advantage of custom com- 
bining is increased at the higher labor rates, and 
larger and larger acreages are required to justify 
owning a combine. 



112 



ZONES OF COST ADVANTAGE: CUSTOM 
COMBINING VS. OWNED T PTO COMBINE 



VALUE OF LABOR PER HOUR ($) 



2.00 



1.00 




50 



100 150 200 

ACRES HARVESTED PER YEAR 



250 



U. S. DEPARTMENT OF AGRICULTURE 



NEC ERS 420-61 (8) ECONOMIC RESEARCH SERVICE 



Figure 2. 



The equal-cost line stops at 250 acres because it 
is not ordinarily feasible to try to cover a larger 
acreage of oats and soybeans in the Mississippi 
Delta with a single 7-foot power- takeoff machine. 
In fact, farm operators in this area who prefer 
to "play it safe"' might try to handle no more 
than 200 acres of these crops in a season. Thus, 
somewhere betwen 200 and 250 acres, depending 
upon the degree of risk aversion of the particular 
farm operator, the equal-cost line loses its rele- 
vance. Cost savings may be more than offset by 
excessive harvesting losses if the least-cost method 
is pushed too far. This is the reason for the clear 
vertical areas of figures 2 and 3. 

The Suggested Analysis Applied to the 
Four Alternatives 

Figure 3 shows least-cost zones for the four al- 
ternative methods of combining. These include 



custom combining, one owned 7- foot power-takeoff 
machine, ownership of two 7-foot power-takeoff 
machines, and ownership of one 12-foot self-pro- 
pelled combine. Interest on the investment in the 
owned machines is again charged at 5 percent in 
the calculations for the upper part of figure 3. 

The calculation of the equal cost points between 
any two of these alternatives is similar to that de- 
scribed above; the two cost functions for a given 
labor rate are set equal to each other and the break- 
even acreage is calculated. 4 This is repeated for 
enough labor rates to enable an equal-cost line to 



* When both alternatives involve fixed costs, the algebra 
is more difficult. For example, the equation for determin- 
ing the equal-cost line between the 12-foot SP and two 
7-foot PTO machines is : 

5(WA+1.83+1.0W=656.25/A+1.40-f0.5W 
in which A represents acreage harvested annually and W 
the value of labor per hour. 



113 



ZONES OF COST ADVANTAGE: FOUR METHODS 
OF COMBINING, MISSISSIPPI DELTA 

WITH INTEREST AT 5 PERCENT 

VALUE OF LABOR PER HOUR ($)^ 




500 



ACRES HARVESTED PER YEAR 



U. S. DEPARTMENT OF AGRICULTURE 



NEC ERS 421-61 (8) ECONOMIC RESEARCH SERVICE 



Figure 3. 



114 



be drawn to separate the least-cost zone of the two 
alternative methods. 

In the upper part of figure 3, the equal-cost line 
between custom combining and one 7-foot owned 
machine is the same as that in figure 2. Above 
about 235 acres, this line becomes the equal-cost 
line between custom combining and use of a 12- 
foot self-propelled machine. With a 5-percent 
interest rate, as used here, two 7- foot combines will 
be the least-cost method only at very low wage 
rates, and with acreages that exceed the capacity 
of one 7- foot machine. 

The cost of a single 7- foot combine will be less 
than that of a 12-foot combine for any acreage, 
so the choice between the two will depend largely 
upon how many acres the farmer thinks he can 
cover with the smaller machine. But even this 
choice will probably not be entirely free of cost 
considerations. Higher labor rates will reduce 
the cost advantage of the 7- foot machine and thus 
reduce the temptation to try to "get by" with it on 
a larger acreage than is safe from the standpoint 
of timeliness. 

Effect of a 15 -Percent Interest Rate 

In the foregoing analysis, a 5-percent interest 
rate was used throughout. But with capital ra- 
tioning and competing uses for capital, the op- 
portunity cost of capital may be considerably 
above the rate paid by farmers on borrowed funds. 

The 15-percent interest rate, of course, enlarges 
the area of advantage of the alternatives involving 
the lesser investments relative to those with the 
greater investments (fig. 3, lower). Thus, it re- 
stricts the zone of a competitive advantage of the 
12-foot self-propelled combine and expands that of 
custom combining. In fact, at the higher labor 
rates, custom combining becomes the least-cost al- 
ternative regardless of the acreage harvested. 

The higher cost of capital may also reenforce 
the farm operator's inclination to try to "get by" 
with a 7-foot combine on more acres than he would 
otherwise attempt to handle. That is, it may push 
to the right our rather indefinite borderland be- 
tween the 7- foot and 12-foot combines, but how 
much is not known. 

Value of a Supplementary Table of Per 
Acre Costs 

"With only two alternatives, construction of the 
chart is simple. But with several alternatives, it 



can become confusing. It is worth while to ar- 
range the data as shown in table 3, showing total 
per acre cost comparisons of the four methods for 
a number of combinations of acreages and labor 
rates. The lowest cost figure for each combination 
shown is boxed and approximate equal-cost lines 
are drawn in. 

This combined table and chart also permits cost 
comparisons within the zone of advantage of each 
method. Thus, we can appraise the cost-penalty 
we would incur by choosing a method other than 
the least-cost one for the particular situation. 

Other Potential Uses of This Method of 
Analysis 

The method is flexible in that there is some 
choice as to which factors to vary and which to 
hold constant. For example, in the analysis above, 
the annual acreage and the wage rate are con- 
sidered as variables and everything else is held 
constant for each chart. A chart showing the 
zones of competitive advantage of the alternatives 
for a given value per hour of labor and for a range 
of interest rates could just as easily have been 
drawn, but the interest rate does not seem to affect 
the zones of advantage to the same extent as the 
wage rate. 

If in a particular situation, the interest rate, 
wage rate, and/or annual acreage can be consid- 
ered as given, equal-cost values can be determined 
for some of the things here considered as fixed. 
For example, combine prices are often subject to 
a certain amount of bargaining, so attention might 
be directed to the maximum price a farmer can 
afford to pay for a particular combine rather 
than hire a custom machine. 

In this instance, the original cost is considered 
a variable. This is one of the elements of fixed 
cost, and the algebra is considerably more in- 
volved. The following notation is used : 

Vi= variable costs per acre of custom combin- 
ing (i.e., the custom rate per acre) ; 

F 2 = annual fixed cost of the owned combine 
(depreciation, interest, taxes, insurance 
and housing) ; 

F 2 = fixed cost per acre of the owned combine ; 

V 2 = variable or operating costs per acre of the 
owned combine and tractor ; 

L 2 = labor requirements in hours per acre with 
owned combine : 



115 



Table 3. — Costs of If. methods of combining for specif ed labor rates and acreages, Mississippi Delta, 

xoith interest at 5 percent x 



Value of labor and method 




Acres harvested per year 








50 


100 


150 


200 


250 


300 


350 


400 


$5 labor: 


Dollars 


Dollars 


Dollars 


Dollars 


Dollars 


Dollars 


Dollars 


Dollars 


Custom combining, 


1 5. 50 1 


1 5. 50 1 




5. 50 1 


1 5. 50 1 


1 5. 50 1 


1 5. 50 1 


1 5. 50 1 


1 5. 50 1 


One 7' owned combine. . 


11. 83 


9. 33 


8. 50 


8. 08 

9. 33 
7. 17 


8. 01 
8. 83 
6. 52 








Two 7' owned combines. . 




8. 50 
6.09 


8.26 
5.78 

#5. 50 
J 


8. 08 


One 12' owned combine 

$4 labor: 


17.02 


10. 46 




8.28 


5.54 

: 'J 


Custom combining 


1 5.501 


1 5. 50 1 


5. 50 1 


1 5. 50 1 


1 5. 50 1 


1 5. 50 1 


5. 50 


One 7' owned combine. 


10. 83 


8. 33 


7. 50 


7.08 
8. 33 
6. 67 


7. 01 
7. 83 
6.02 










7. 50 
5 59 

# 5. 50 
Jr. 


If 7.26 


7. 08 


One 12' owned combine 


16. 52 


9. 96 


7. 78 


A 1 5.281 


I 5. 04 


$3 labor: 






5. 50 




Custom combining.. . . 


1 5. 50 1 


1 5. 501 


5. 50 1 


1 5. 50 | 


1 5. 501 


5. 50 


One 7' owned combine 


9. 83 


7. 33 


6. 50 


6. 08 
7.33 
6. 17 

■ -> 50 


6. 01 
6. 83 
5.52, 

5. 50 
1 5. Oil 








,# 6. 50 


6. 26 


6. 08 


One 12' owned combine 


16. 02 


9. 46 


7. 28 


W 1 5. 09| 


1 4.781 


1 4.54 


$2 labor: 






% 5.50 
m 


5. 50 




Custom combining. 


1 5. 501 


1 5. 50 1 




5. 50, 
5.M 


5.50 


One 7' owned combine 


8. 83 
"""l5.52 _ 


6. 33 

8.96" 

,...«■ 

^# : S'. 50 


' 1 5. 08 1 




Two 7' owned combines 


^6.78 


6. 33 
5. 67 

5. 50 


5. 83 
5. 02 

5. 50 


i 5. 50 


5. 26 


5.08 


One 12' owned combine 


i 1 4.591 


1 4.281 


i 4.04 


$1 labor: 


1 5.50 

If' 4 50 


5. 50 
""4." 26" 




Custom combining.. . . 


1 5. 501 




5.50 


5. 50 


One 7' owned combine 


7. 83 


#1 5.331 


4. 50 1 


1 4. 08 1 


1 4. OH 




Two 7' owned combines . 


t 




5. 33 
5. 17 


4. 83 
4. 52 


4. 08 


One 12' owned combine 


15. 02j 


' _ 8. 46 




M 1 4.091 


1 3. 781 


1 3.54 








¥:? 







1 □ — indicates minimum cost. The curved -line separates the 3 zones of cost advantage. 



W= the value of labor per hour ; 
C 2 = original cost of the owned combine ; 
Y 2 = expected useful life of the owned com- 
bine, in years ; 
r= opportunity cost of capital, or the an- 
nual interest rate ; 
= cost of taxes, insurance, and housing, as 
an annual rate ; and 
A= acres to be harvested per year. 

The total fixed cost is the sum of annual depre- 
ciation (0.9C 2 /Y 2 ), interest on investment (C 2 r), 

~2~ 
and taxes, insurance, and housing (0.01 C2). 

Thus 



F 2 =0.9C 2 /Y 2 + C 2 r/2+0.0lC 2 



Therefore, 

^ _ 0.9C 2 /Y 2 + C 2 r/2 + 0.0lC 2 
F 2 ^ 

The two cost functions are set equal to each 
other : 



V 1 =F 2 +V 2 +L 2 W 

_0.9C 2 /Y 2 + C 2 r/2+0.0lC 2 



Since the idea is to determine the break-even orig- 
inal cost, or what the farmer can afford to pay 
for a combine (with a given custom rate, interest 
rate, labor rate, acreage, and useful life), this 
equation is solved for C 2 : 

_ A(V 1 -V 2 -L 2 W) 
^ 2 (0.9/Y 2 + r/2 + t) 

Again, while the expected useful life of a com- 
bine is arbitrarily set at 10 years in this analysis, 
the appropriate depreciation rate for a real-life 
situation is highly individual and subjective, and 
very difficult to determine. Thus it may be help- 
ful, when other coefficients are known with greater 
certainty, to determine the number of years of 
use the owned combine would need to give to 
make it competitive with hiring a custom machine. 

Using the same notation as above, the two cost 
functions are again set equal to each other. But 
this time the question involves the break-even 
number of years of useful life (with everything 
else given), so the equation is solved for Y 2 , thus : 



+v 2 +uw 



Y 2 = 



0.9C 2 



[A(Vx-V 2 -L 2 W) -C 2 (r/2+t)] 



116 



Although this discussion of the use of the sug- 
gested analytical procedure has been in terms of 
hiring vs. owning a combine, this analytical 
method can prove equally helpful in making 
sound choices involving a variety of other farm 
machines and other managerial decisions. Re- 
gardless of the particular problem to which this 



analytical method is applied, however, it enables 
the economic analyst to take into account more 
variables than does the conventional method. This 
means that, in any particular application, the 
suggested method facilitates the determination of 
a least-cost alternative over a wide variety of 
circumstances. 



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